Abstract

An integro-differential equation for the three dimensional shape of air–water interface on superhydrophobicsurfaces comprised of pores with arbitrary shapes and depths is developed and used to predict the static critical pressure under which such surfaces depart from the non-wetting state. Our equation balances the capillary forces with the pressure of the air entrapped in the pores and that of the water over the interface. Stability of shallow and deep circular, elliptical, and polygonal pores is compared with one another and a general conclusion is drawn for designing pore shapes for superhydrophobicsurfaces with maximum stability.

Received 21 October 2011Accepted 09 December 2011Published online 04 January 2012

Acknowledgments:

The authors would like to acknowledge the financial support for this work provided Defense Advanced Research Projects Agency (DARPA) Contract No. W91CRB-10-1-0003. In addition, BE and HVT also acknowledge VCU Presidential Research Incentive Program (PRIP) for partial support. The authors acknowledge Professor Bandyopadhyay of VCU School of Engineering for Fig. 1(a).